arXiv subjects

Ad Lagendijk

Publications and source records attributed to Ad Lagendijk.

At least 19 recordsLinked to original sources

arXiv2026

Defect states in three-dimensional diamond photonic band gap crystals

We perform a theoretical study of defect states within the photonic band gap of three-dimensional diamond crystals composed of point scatterers and doped with substitutional defects. The defects introduce localized states inside the photonic band gap, whose existence conditions and eigenfrequencies are expressed in terms of the on-site Green's function of the ideal defect-free crystal. Off-site Green's functions are also calculated as function of distance and are shown to vanish within approximately two unit cells. Finite-size effects are analyzed by comparing the results obtained in the infinite-crystal limit with numerical simulations based on the coupled-dipole method. The latter not only reproduce the eigenfrequencies of the defect states within the band gap, but also provide their lifetimes originating from the finite crystal size. The lifetimes of the defect states increase exponentially with crystal size, becoming very long for large crystals. In addition to defect states in the three-dimensional photonic band gap, the defects also give rise to strongly detuned states outside the gap, which decouple from the spectrum of the ideal defect-free crystal.

cond-mat.dis-nn↗

arXiv2026

Optically dense nanowire metamaterials are transparent to polarization

We study the transport of light through dense opaque anisotropic metamaterials consisting of oriented nanowires. The nanowires consist of polymer photoresist that is structured by direct laser writing (DLW) with two-photon induced polymerization, with radii between $a = 0.5$ and $1~\mu \text{m}$. Our flat samples have a thickness up to 9 layers, from $L = 3~\mu \text{m}$ to $20~\mu \text{m}$. Within each layer, the nanowires are parallel and spaced with random nearest-neighbor distances; nanowires in adjacent layers are perpendicular. The diffuse optical transmission at $\lambda = 633~$nm is as low as $T = 12 \%$, typical of optically dense, multiple scattering metamaterials, with a mean free path down to $\ell = 1.1~\mu \text{m}$, much less than the sample thickness. It is striking that the linear polarization of the input light is maintained at the output of the dense nanowire samples, and not scrambled as in dense nanosphere arrays. Moreover, the linear output polarization faithfully tracks the input polarization. We propose that the polarization is maintained in our optically thick samples, since light is predominantly transported perpendicularly to the nanowire layers. The polarization vector then lies in the nanowire plane, consisting of a linear combination of parallel and perpendicular vectors that are both conserved upon subsequent scattering. Hence, the polarization remains independent of nanowire orientation, even after multiple scattering events. We propose that anisotropic scattering samples may find practical uses in white LEDs and its applications in lighting luminaires, optical communication, and encryption systems.

physics.optics↗

arXiv2025

Radiative local density of states in three-dimensional photonic band-gap crystals to interpret time-resolved emission

We investigate the spontaneous emission of light in three-dimensional (3D) photonic crystals through theoretical calculations and simulations. It is well known that spontaneous emission depends on the radiative local density of states (RLDOS). Photonic band-gap crystals radically modulate the RLDOS, thereby controlling spontaneous emission. We compare two different methods to calculate the RLDOS: the plane-wave expansion (PWE) method and the finite-difference time-domain (FDTD) method. The PWE method directly calculates the RLDOS of an infinite photonic crystal, whereas the FDTD method simulates the RLDOS through the power emitted by a dipole in a finite photonic crystal. We demonstrate that the methods yield similar frequency-dependent trends in the RLDOS, with relative differences of less than 12% that originate from the different boundary conditions. We employ the plane-wave expansion method to compute distributions of emission rates that are relevant to many optical experiments where quantum emitters are distributed within a crystal. Such distributions of emission rates enable us to compute and directly interpret the time-resolved decay as observed in experiments. We expect that our results promote the RLDOS to the realm of optical design and products.

physics.optics↗

arXiv2025

Momentum-resolved reflectivity of a 2D photonic crystal in the near-infrared

Two-dimensional (2D) photonic crystals offer strong control over the propagation of light through their bands. Theoretical methods for computing the band structure in 2D are well-established and fast because 2D photonic crystals are homogeneous in the third dimension. Experimental verification is scarce, however, especially in the telecom range, because real photonic crystals and experimental methods inherently cannot be homogeneous in the third dimension. In this work, we report momentum-resolved reflectivity measurements on photonic crystals that are periodic in two dimensions and homogeneous over a thickness of 5 {\mu}m. Using Fourier spectroscopy, we carefully select wave vectors in the 2D plane of periodicity of the photonic crystal. Our experiments agree excellently with 2D band structure calculations and with 2D finite-difference time-domain simulations, confirming that our experimental methods truly pertain to nanophotonics in 2D. Our results provide a robust bridge between theory and experiment, and our techniques can be readily extended to other 2D structures, including those with functional defects.

physics.optics↗

arXiv2025

Resolving features and derivatives in noisy data using weighted Whittaker-Henderson smoothing

A frequently occurring challenge in experimental and numerical observations is how to resolve features, such as spectral peaks - with center, width, height - and derivatives from measured data with unavoidable noise. Although many smoothing procedures exist, most are ineffective at reducing noise when the widths of the features varies strongly. Therefore, we modify the Whittaker-Henderson smoothing procedure to locally balance the spectral features and the noise. The central contribution of our procedure is that we introduce adjustable weights that are optimized using cross-validation. Using the measurement errors, a straightforward error analysis of the smoothed results is feasible. To illustrate the effectiveness of our smoothing algorithm, we derive for an optical Bragg reflector nanostructure the chirp of an optical pulse (group delay dispersion) using synthetic phase data with noise. The smoother faithfully reconstructs the group delay dispersion, reducing noise by more than a factor 40, allowing to identify details that otherwise remain buried in noise. Finding the optimal weights using the limited-memory BFGS algorithm for N=1000 complex valued reflectivity data points takes on average less than two seconds on a typical computer. To further illustrate the power of our smoother, we introduce a general framework to solve commonly occurring difficulties in data and data analysis; how to properly smoothen unequally sampled data, how to identify and quantify discontinuities, including discontinuous derivatives or kinks, how to properly smooth data in the vicinity of boundaries to the data domains, and multi-dimensional smoothing.

physics.data-an↗

arXiv2025

Dispersion of backward-propagating waves in a surface defect on a 3D photonic band gap crystal

We experimentally study the dispersion relation of waves in a two-dimensional (2D) defect layer with periodic nanopores that sits on a three-dimensional (3D) photonic band gap crystal made from silicon by CMOS-compatible methods. The nanostructures are probed by momentum-resolved broadband near-infrared imaging of p-polarized reflected light that is collected inside the light cone as a function of off-axis wave vectors. We identify surface defect modes at frequencies inside the band gap with a narrow relative linewidth ($\Delta\omega/\omega$ = 0.028), which are absent in defect-free 3D crystals. We calculate the dispersion of modes with relevant mode symmetries using a plane-wave-expansion supercell method with no free parameters. The calculated dispersion matches very well with the measured data. The dispersion is negative in one of the off-axis directions, corresponding to backward-propagating waves where the phase velocity and the group velocity point in opposite directions, as confirmed by finite-difference time-domain simulations. We also present an analytic model of a 2D grating sandwiched between vacuum and a negative real $\epsilon'$ < 0 that mimics the 3D photonic band gap. The model's dispersion agrees with the experiments and with the fuller theory and shows that the backward propagation is caused by the surface grating. We discuss possible applications, including a device that senses the output direction of photons emitted by quantum emitters in response to their frequency.

physics.optics↗

arXiv2024

Experimentally mapping the scattering phases and amplitudes of a finite object by optical mutual scattering

Mutual scattering arises when multiple waves intersect within a finite scattering object, resulting in cross-interference between the incident and scattered waves. By measuring mutual scattering, we determine the complex-valued scattering amplitude $f$ - both amplitude and phase - of the finite object, which holds information on its scattering properties by linking incident and outgoing waves from any arbitrary direction. Mutual scattering is present for any coherent wave - acoustic, electromagnetic, particle - and we here demonstrate the effect using optical experiments. We propose an experimental technique for characterization that utilizes mutual scattering and we present our results for four distinct finite objects: a polystyrene sphere (diameter $59\ \mu$m), a single black human hair (diameter $92\ \mu$m), a strip of pultruded carbon (edge length $140\ \mu$m), and a block of ZnO$_2$ (edge length $64\ \mu$m). Our measurements exhibit qualitative agreement with Mie scattering calculations where the model is applicable. Deviations from the model indicate the complexity of the objects, both in terms of their geometrical structure and scattering properties. Our results offer new insights into mutual scattering and have significant implications for future applications of sample characterization in fields such as metrology, microscopy, and nanofabrication.

physics.optics↗

arXiv2024

Probing the position-dependent optical energy fluence rate in three-dimensional scattering samples

The accurate determination of the position-dependent energy fluence rate of scattered light (which is proportional to the energy density) is crucial to the understanding of transport in anisotropically scattering and absorbing samples, such as biological tissue, seawater, atmospheric turbulent layers, and light-emitting diodes. While Monte Carlo simulations are precise, their long computation time is not desirable. Common analytical approximations to the radiative transfer equation (RTE) fail to predict light transport and could even give unphysical results. Therefore, we experimentally probe the position-dependent energy fluence rate of light inside scattering samples where the widely used P1 and P3 approximations to the RTE fail. The samples are three-dimensional (3D) aqueous suspensions of anisotropically scattering and both absorbing and non-absorbing spherical scatterers, namely, microspheres (r = 0.5 um) with and without absorbing dye. To probe the energy fluence rate, we detect the emission of quantum-dot reporter particles that are excited by the incident light and that are contained in a thin capillary. By scanning the capillary through the sample, we access the position dependence. We present a comprehensive discussion of experimental limitations and of both random and systematic errors. Our observations agree well with the Monte Carlo simulations and the P3 approximation of the RTE with a correction for forward scattering. In contrast, the P1 and the P3 approximations deviate increasingly from our observations, ultimately even predicting unphysical negative energies.

physics.optics↗

arXiv2023

Symmetries and Wavefunctions of Photons Confined in 3D Photonic Band Gap Superlattices

We perform a computational study of confined photonic states that appear in a three-dimensional (3D) superlattice of coupled cavities, resulting from a superstructure of intentional defects. The states are isolated from the vacuum by a 3D photonic band gap, using a diamond-like inverse woodpile crystal structure, and exhibit 'Cartesian' hopping of photons in high-symmetry directions. We investigate the confinement dimensionality to verify which states are fully 3D confined, using a recently developed scaling theory to analyze the influence of the structural parameters of the 3D crystal. We create confinement maps that trace the frequencies of 3D confined bands for select combinations of key structural parameters, namely the pore radii of the underlying regular crystal and of the defect pores. We find that a certain minimum difference between the regular and defect pore radii is necessary for 3D confined bands to appear, and that an increasing difference between the defect pore radii from the regular radii supports more 3D confined bands. In our analysis we find that their symmetries and spatial distributions are more varied than electronic orbitals known from solid state physics. We also discover pairs of degenerate 3D confined bands with p-like orbital shapes and mirror symmetries matching the symmetry of the superlattice. Finally, we investigate the enhancement of the local density of optical states (LDOS) for cavity quantum electrodynamics (cQED) applications. We find that donor-like superlattices, i.e., where the defect pores are smaller than the regular pores, provide greater enhancement in the air region than acceptor-like structures with larger defect pores, and thus offer better prospects for doping with quantum dots and ultimately for 3D networks of single photons steered across strongly-coupled cavities.

physics.optics↗

arXiv2023

Wavefront shaping through a free-form scattering object

Wavefront shaping is a technique to study and control light transport inside scattering media. Wavefront shaping is considered to be applicable to any complex material, yet in most previous studies, the only sample geometries that are studied are slabs or wave-guides. In this paper, we study how macroscopic changes in the sample shape affect light scattering using the wavefront shaping technique. Using a flexible scattering material, we optimize the intensity of light in a focusing spot using wavefront shaping and record the optimized pattern, comparing the enhancement for different curvatures and beam radii. We validate our hypothesis that wavefront shaping has a similar enhancement regardless of the free-form shape of the sample and thus offers relevant potential for industrial applications. We propose a new figure of merit to evaluate the performance of wavefront shaping for different shapes. Surprisingly, based on this figure of merit, we observe that for this particular sample, wavefront shaping has a slightly better performance for a free-form shape than for a slab shape.

physics.optics↗

arXiv2022

Sensing the position of a single scatterer in an opaque medium by mutual scattering

We investigate the potential of mutual scattering, i.e., light scattering with multiple properly phased incident beams, as a method to extract structural information from inside an opaque object. In particular, we study how sensitively the displacement of a single scatterer is detected in an optically dense sample of many (up to $N=1000$) similar scatterers. By performing exact calculations on ensembles of many point scatterers, we compare the mutual scattering (from two beams) and the well-known differential cross-section (from one beam) in response to the change of location of a single dipole inside a configuration of randomly distributed similar dipoles. Our numerical examples show that mutual scattering provides speckle patterns with an angular sensitivity at least 10 times higher than the traditional one-beam techniques. By studying the "susceptivity" of mutual scattering, we demonstrate the possibility to determine the original depth relative to the incident surface of the displaced dipole in an opaque sample. Furthermore, we show that mutual scattering offers a new approach to determine the complex scattering amplitude.

physics.optics↗

arXiv2022

Scaling theory of wave confinement in classical and quantum periodic systems

Functional defects in periodic media confine waves - acoustic, electromagnetic, electronic, spin, etc. - in various dimensions, depending on the structure of the defect. While defects are usually modelled by a superlattice with a typical band-structure representation of energy levels, determining the confinement associated with a given band is highly non-trivial and no analytical method is known to date. Therefore, we propose a rigorous method to classify the dimensionality of the confinement. Starting from the confinement energy and the mode volume, we use finite-size scaling to find that ratios of these quantities to certain powers yield the confinement dimensionality of each band. This classification has negligible additional computational costs compared to a band structure calculation and is valid for any type of wave in both quantum and classical regimes, and any dimension. In the quantum case, we illustrate our method on electronic confinement in 2D hexagonal BN with a nitrogen vacancy, which confirms the previous results. In the classical case, we study a three-dimensional photonic band gap cavity superlattice, where we identify novel acceptor-like behavior.

cond-mat.dis-nn↗

arXiv2021

Breakdown of light transport models in photonic scattering slabs with strong absorption and anisotropy

The radiative transfer equation (RTE) models the transport of light inside photonic scattering samples such as paint, foam and tissue. Analytic approximations to solve the RTE fail for samples with strong absorption and dominant anisotropic scattering and predict unphysical negative energy densities and the diffuse flux in the wrong direction. Here we fully characterize the unphysical regions of three popular approximations to the RTE for a slab, namely the $P_1$ approximation (or diffusion approximation), the $P_3$ approximation, and a popular modification to $P_3$ that corrects the forward scattering in the approximation. We find that the delta function correction to $P_3$ eliminates the unphysical range in the forward scattering. In addition, we compare the predictions of these analytical methods to exact Monte Carlo simulations for the physical and unphysical regions. We present maps of relative errors for the albedo and the anisotropy of the scatterers for a realistic index contrast typical of a polymer slab in air and optical thickness. The relative error maps provide a guideline for the accuracy of the analytical methods to interpret experiments on light transport in photonic scattering slabs. Our results show that the $P_1$ approximation is significantly inaccurate to extract transport parameters unless the sample scatters purely isotropic and elastic. The $P_3$ approximation exceeds $P_1$ in terms of accuracy in its physical range for moderate absorption, and the $P_3$ with the delta function correction is the most accurate approximation considered here for the forward direction.

physics.optics↗

arXiv2021

Observation of mutual extinction and transparency in light scattering

Interference of scattered waves is fundamental for modern light-scattering techniques, such as optical wavefront shaping. Recently, a new type of wavefront shaping was introduced where the extinction is manipulated instead of the scattered intensity. The underlying idea is that upon changing the phases or the amplitudes of incident beams, the total extinction will change due to interference described by the cross terms between different incident beams. Here, we experimentally demonstrate the mutual extinction and transparency effects in scattering media, in particular, a human hair and a silicon bar. To this end, we send two light beams with a variable mutual angle on the sample. Depending on the relative phase of the incident beams we observe either nearly zero extinction, mutual transparency, or almost twice the single-beam extinction, mutual extinction, in agreement with theory. We use an analytical approximation for the scattering amplitude, starting from a completely opaque object and we discuss the limitations of our approximation. We discuss the applications of the mutual extinction and transparency effects in various fields such as non-line-of-sight communications, microscopy, and biomedical imaging.

physics.optics↗

arXiv2019

Universal Validity Ranges of Diffusion Theory for Light and Other Electromagnetic Waves

The well-known diffusion theory describes propagation of light and electromagnetic waves in complex media. While diffusion theory is known to fail both for predominant forward scattering or strong absorption, its precise range of validity has never been established. Therefore we present precise, universal limits on the scattering properties, beyond which diffusion theory yields unphysical negative energy density and negative incident flux. When applying diffusion theory to samples outside validity ranges to {\it infer} scattering properties from transmission and reflection, the resulting transport parameters deviate by up to an order of magnitude compared to the true ones. These discrepancies are relevant to atmospheric and climate sciences, biophysics and health sciences, white LEDs and lighting, and Anderson localization of waves.

physics.optics↗

arXiv2019

Systematic design of the color point of a white LED

Lighting is a crucial technology that is used every day. The introduction of the white light emitting diode (LED) that consists of a blue LED combined with a phosphor layer, greatly reduces the energy consumption for lighting. Despite the fast-growing market white LED's are still designed using slow, numerical, trial-and-error algorithms. Here we introduce a radically new design principle that is based on an analytical model instead of a numerical approach. Our design model predicts the color point for any combination of design parameters. In addition the model provides the reflection and transmission coefficients - as well as the energy density distribution inside the LED - of the scattered and re-emitted light intensities. To validate our model we performed extensive experiments on an emblematic white LED and found excellent agreement. Our model provides for a fast and efficient design, resulting in reduction of both design and production costs.

physics.optics↗

arXiv2018

Finite size scaling of density of states in photonic bandgap crystals

The famous vanishing of the density of states (DOS) in a band gap, be it photonic or electronic, pertains to the infinite-crystal limit. In contrast, all experiments and device applications refer to finite crystals, which raises the question: Upon increasing the linear size $L$ of a crystal, how fast does the DOS approach the infinite-crystal limit? We present a theory for finite crystals that includes Bloch-mode broadening due to the presence of crystal boundaries. Our results demonstrate that the DOS for frequencies inside a band gap has a $1/L$ scale dependence for crystals in one, two and three dimensions.

physics.optics↗

arXiv2017

3D spatially-resolved optical energy density enhanced by wavefront shaping

We study the three-dimensional (3D) spatially-resolved distribution of the energy density of light in a 3D scattering medium upon the excitation of open transmission channels. The open transmission channels are excited by spatially shaping the incident optical wavefronts. To probe the local energy density, we excite isolated fluorescent nanospheres distributed inside the medium. From the spatial fluorescent intensity pattern we obtain the position of each nanosphere, while the total fluorescent intensity gauges the energy density. Our 3D spatially-resolved measurements reveal that the local energy density versus depth (z) is enhanced up to 26X at the back surface of the medium, while it strongly depends on the transverse (x; y) position. We successfully interpret our results with a newly developed 3D model that considers the time-reversed diffusion starting from a point source at the back surface. Our results are relevant for white LEDs, random lasers, solar cells, and biomedical optics.

physics.optics↗